Subgroups — C₃×#21370 #10639977

Order 768.

780 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#1950	C₂	1	4	yes	maximal, complemented
5	C₃×#1855	C₂	1	4	yes	maximal
6	C₃×C₄×#108	C₂	1	4	yes	maximal, complemented
7	#21370	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₃×#432	—	2	1	no	—
11	C₃×#432	—	2	1	no	—
12	C₃×#431	—	2	1	no	—
13	C₃×#431	—	2	1	no	—
14	C₃×#431	C₄	1	2	yes	—
15	C₃×#431	C₄	1	2	yes	—
16	C₃×#431	C₄	1	2	yes	—
17	C₃×#431	C₄	1	2	yes	—
18	C₂×C₃×#108	C₂²	1	8	yes	—
19	C₃×#423	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₃×#407	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₃×C₄×M₁₆	—	2	1	no	—
24	C₃×C₄×M₁₆	—	2	1	no	—
25	C₃×C₄×M₁₆	C₂²	1	2	yes	—
26	C₃×C₄×M₁₆	C₂²	1	2	yes	—
27	C₃×C₄×M₁₆	C₂²	1	2	yes	—
28	C₂×C₃×#97	—	2	1	no	—
29	C₂×C₃×C₄×C₈	—	2	1	no	—
30	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
31	C₃×#341	C₂²	1	8	yes	—
32	#2920	C₂×C₃	1	1	yes	characteristic
33	C₂×#431	C₂×C₃	1	1	yes	characteristic
34	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
35	#1950	C₂×C₃	1	4	yes	complemented
36	#1855	C₂×C₃	1	4	yes	—
37	C₄×#108	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
39	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
40	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃×M₁₆	—	2	2	no	—
42	C₂×C₃×M₁₆	—	2	8	no	—
43	C₂×C₃×M₁₆	C₂³	1	4	yes	—
44	C₂×C₃×M₁₆	C₂³	1	4	yes	—
45	C₂²×C₃×C₈	—	2	2	no	—
46	C₂²×C₃×C₈	C₂³	1	4	yes	—
47	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
52	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
53	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
54	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
55	C₂×C₃×C₄²	Q₈	1	1	yes	characteristic
56	C₂×C₃×C₄²	Q₈	1	1	yes	characteristic
57	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
59	C₃×#108	—	2	16	no	—
60	C₃×C₄⋊C₈	—	2	2	no	—
61	C₃×C₄⋊C₈	—	2	2	no	—
62	C₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₃×C₂²⋊C₈	—	2	2	no	—
65	C₃×C₂²⋊C₈	—	2	2	no	—
66	C₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
67	C₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
68	C₃×#97	—	2	2	no	—
69	C₃×#97	—	2	2	no	—
70	C₃×#97	—	2	2	no	—
71	C₃×C₄×C₈	—	2	2	no	—
72	C₃×C₄×C₈	—	2	2	no	—
73	C₃×C₄×C₈	—	2	2	no	—
74	C₃×C₄×C₈	C₂×C₄	1	4	yes	—
75	C₃×C₄×C₈	C₂×C₄	1	4	yes	—
76	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
77	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
78	#432	—	2	1	no	—
79	#432	—	2	1	no	—
80	#431	—	2	1	no	—
81	#431	—	2	1	no	—
82	#431	C₃×C₄	1	2	yes	—
83	#431	C₃×C₄	1	2	yes	—
84	#431	C₃×C₄	1	2	yes	—
85	#431	C₃×C₄	1	2	yes	—
86	C₂×#108	C₂²×C₃	1	8	yes	—
87	#423	C₂²×C₃	1	2	yes	—
88	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
89	#407	C₂²×C₃	1	2	yes	—
90	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
91	C₄×M₁₆	—	2	1	no	—
92	C₄×M₁₆	—	2	1	no	—
93	C₄×M₁₆	C₂²×C₃	1	2	yes	—
94	C₄×M₁₆	C₂²×C₃	1	2	yes	—
95	C₄×M₁₆	C₂²×C₃	1	2	yes	—
96	C₂×#97	—	2	1	no	—
97	C₂×C₄×C₈	—	2	1	no	—
98	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
99	#341	C₂²×C₃	1	8	yes	—
100	C₂⁴×C₃	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₃×C₄	—	2	4	no	—
102	C₂²×C₃×C₄	—	2	4	no	—
103	C₂²×C₃×C₄	—	4	2	no	—
104	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
122	C₃×M₁₆	—	2	8	no	—
123	C₃×M₁₆	—	2	4	no	—
124	C₃×M₁₆	—	2	8	no	—
125	C₃×M₁₆	#41	1	8	yes	—
126	C₂×C₃×C₈	—	2	8	no	—
127	C₂×C₃×C₈	—	2	4	no	—
128	C₂×C₃×C₈	—	2	8	no	—
129	C₂×C₃×C₈	—	2	4	no	—
130	C₂×C₃×C₈	C₂²×C₄	1	8	yes	—
131	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
132	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
133	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
134	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
135	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
136	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
137	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
138	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
139	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
140	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
141	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
142	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
143	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
144	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
145	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
146	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₄	C₃×Q₈	1	1	yes	characteristic
148	C₂³×C₄	C₃×Q₈	1	1	yes	characteristic
149	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	2	8	no	—
152	C₂×M₁₆	C₂³×C₃	1	4	yes	—
153	C₂×M₁₆	C₂³×C₃	1	4	yes	—
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	C₂³×C₃	1	4	yes	—
156	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
160	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
161	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
162	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
163	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
164	C₂×C₄²	C₃×Q₈	1	1	yes	characteristic
165	C₂×C₄²	C₃×Q₈	1	1	yes	characteristic
166	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
168	#108	—	2	16	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	C₂×C₃×C₄	1	4	yes	—
172	C₄⋊C₈	C₂×C₃×C₄	1	4	yes	—
173	C₂²⋊C₈	—	2	2	no	—
174	C₂²⋊C₈	—	2	2	no	—
175	C₂²⋊C₈	C₂×C₃×C₄	1	4	yes	—
176	C₂²⋊C₈	C₂×C₃×C₄	1	4	yes	—
177	#97	—	2	2	no	—
178	#97	—	2	2	no	—
179	#97	—	2	2	no	—
180	C₄×C₈	—	2	2	no	—
181	C₄×C₈	—	2	2	no	—
182	C₄×C₈	—	2	2	no	—
183	C₄×C₈	C₂×C₃×C₄	1	4	yes	—
184	C₄×C₈	C₂×C₃×C₄	1	4	yes	—
185	C₂³×C₃	—	2	2	no	—
186	C₂³×C₃	—	2	2	no	—
187	C₂³×C₃	—	4	1	no	—
188	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂³×C₃	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₃×C₄	—	2	2	no	—
192	C₂×C₃×C₄	—	2	2	no	—
193	C₂×C₃×C₄	—	2	2	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	2	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	2	no	—
202	C₂×C₃×C₄	—	2	2	no	—
203	C₂×C₃×C₄	—	2	2	no	—
204	C₂×C₃×C₄	—	4	1	no	—
205	C₂×C₃×C₄	—	4	1	no	—
206	C₂×C₃×C₄	—	4	1	no	—
207	C₂×C₃×C₄	#108	1	4	yes	complemented
208	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂×#41	1	4	yes	—
221	C₃×C₈	—	2	8	no	—
222	C₃×C₈	—	2	8	no	—
223	C₃×C₈	—	4	4	no	—
224	C₂⁴	C₂×C₃×Q₈	1	1	yes	characteristic
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
230	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
231	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
234	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
245	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
246	M₁₆	—	2	8	no	—
247	M₁₆	—	2	4	no	—
248	M₁₆	—	2	8	no	—
249	M₁₆	C₃×#41	1	8	yes	—
250	C₂×C₈	—	2	8	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	8	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	C₂²×C₃×C₄	1	8	yes	—
255	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
256	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
257	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
258	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
259	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
260	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
261	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
262	C₄²	C₃×C₄⋊C₄	1	1	yes	characteristic
263	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
268	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
269	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
270	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	4	4	no	—
279	C₂²×C₃	C₂×#108	1	2	yes	—
280	C₂²×C₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
281	C₂²×C₃	#533	1	2	yes	—
282	C₃×C₄	—	2	1	no	—
283	C₃×C₄	—	2	1	no	—
284	C₃×C₄	—	2	1	no	—
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	C₂×#108	1	2	yes	—
290	C₃×C₄	C₂×#108	1	2	yes	—
291	C₃×C₄	#430	1	2	yes	—
292	C₃×C₄	C₄×#41	1	2	yes	—
293	C₃×C₄	#525	1	2	yes	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	4	1	no	—
297	C₂³	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
298	C₂³	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
299	C₂³	C₂²×C₃×Q₈	1	1	yes	characteristic
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	C₃×#108	1	4	yes	complemented
317	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
319	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
321	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
322	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₃×#41	1	4	yes	—
330	C₈	—	2	8	no	—
331	C₈	—	2	8	no	—
332	C₈	—	4	4	no	—
333	C₂×C₃	—	2	2	no	—
334	C₂×C₃	—	2	2	no	—
335	C₂×C₃	—	4	1	no	—
336	C₂×C₃	#2296	1	1	yes	characteristic
337	C₂×C₃	C₂²×#108	1	1	yes	characteristic
338	C₂×C₃	C₂×#430	1	1	yes	characteristic
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	4	4	no	—
347	C₂²	C₂×C₃×#108	1	2	yes	—
348	C₂²	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
349	C₂²	C₃×#533	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	C₂×C₃×#108	1	2	yes	—
358	C₄	C₂×C₃×#108	1	2	yes	—
359	C₄	C₃×#430	1	2	yes	—
360	C₄	C₃×C₄×#41	1	2	yes	—
361	C₄	C₃×#525	1	2	yes	—
362	C₃	#21370	1	1	yes	characteristic, direct product factor, Sylow
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	4	1	no	—
366	C₂	C₃×#2296	1	1	yes	characteristic
367	C₂	C₂²×C₃×#108	1	1	yes	characteristic
368	C₂	C₂×C₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ C₂²×C₃×C₄² ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₃×#1950	C₂	semidirect
6. C₃×C₄×#108	C₂	semidirect
7. #21370	C₃	direct (N × H)
35. #1950	C₂×C₃	semidirect
37. C₄×#108	C₂×C₃	semidirect
207. C₂×C₃×C₄	#108	semidirect
316. C₂×C₄	C₃×#108	semidirect
362. C₃	#21370	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#2920	2
C₂×C₃×#431	2
C₂×C₃×C₄×M₁₆	2
C₃×#1950	2
C₃×#1855	2
C₃×C₄×#108	2
#21370	3

Subgroups — C3×#21370 #10639977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21370 #10639977